The Normal Distribution
On a province wide mathematics exam, the mean was 65 and the standard deviation was 15. The marks were determined to be normally distributed. Describe the distribution of marks on the exam. Where do the marks lie?
We are given that the mean was `bar(x)=65` and the standard deviation s=15. Also we know that the marks are normally distributed.
Then by the empirical normal rule we know that approximately 68% of teh marks will lie within 1 standard deviation of the mean, approximately 95% of the marks will lie within 2 standard deviations of the mean, and approximately 99.7% of the marks will lie within 3 standard deviations of the mean.
Then about 68% of the marks will be between 50 and 80, 95% will be between 35 and 95, and 99.7% will be between 20 and 110.